Sur la fonction croissance des variétés riemanniennes

Nous donnons un aperçu du degré de différentiabilité de la fonction croissance des variétés riemanniennes ainsi que de ses singularités en dimension 2.

Differentiability properties of the isoperimetric profile and topology of analytic Riemannian manifolds.

Abstract: We show that smooth isoperimetric profiles are exceptional for real analytic Riemannian manifolds. For instance, under some extra assumptions, this can happen only on topological spheres

Topologie à l'infini et variétés à géométrie bornée

We give a quick review on the asymptotic topology and the geometry of manifolds with bounded geometry, by quoting also some results obtained by the authors.

Some remarks on universal covers and groups

We give a quick reviw of problems concerning the topological behavior of contractible covering spaces, from the point of view of the topology at infinity.

Regularity of isoperimetric profiles

In this short paper we summerize some results about the analyticity of isoperimetric profiles recently appeared in the specialized literature.

A short survey on isoperimetric problem on non compact Riemannian manifolds

In this text, we explain some known results about isoperimetric profile of complete smooth noncompact Riemannian manifolds of dimension 2, with one end, with two ends and with more than two ends.

Sur la croissance des variétés à géométrie bornée

Nous survolons quelques résultats obtenus par les auteurs sur les variétés à géométrie bornée et croissance lineaire et sur les types de croissance possibles des variétés à géométrie bornée.

Bounded Geometry, Growth and Topology

The ends of manifolds with bounded geometry and linear growth

We prove that simply connected open manifolds of bounded geometry, linear growth and sublinear filling growth (e.g. finite filling area) are simply connected at infinity.

Calibrations and isoperimetric profiles

We equip many noncompact nonsimply connected surfaces with smooth Riemannian metrics whose isoperimetric profile is smooth, a highly nongeneric property. The computation of the profile is based on a calibration argument, a rearrangement argument, the Bol-Fiala curvature dependent inequality, together with new results on the profile of surfaces of revolution and some hardware know-how.